Autonomous Memory Folding

• Autonomous memory folding is the process by which learning systems self-organize and compress internal representations, preserving essential sensory and semantic details.
• It utilizes unsupervised methods such as coherent projection and cubical complex transformations to achieve minimal and robust memory models with quadratic efficiency.
• Applications span adaptive robotics, transformer optimization, and continual learning, enabling systems to maintain context and reduce resource usage in dynamic environments.

Autonomous memory folding refers to mechanisms by which learning systems—biological, artificial, or material—self-organize, compress, and restructure internal memory representations without external supervision, optimizing for efficiency, adaptability, and relevance to future behavior or goals. A diverse body of research has established rigorous algorithmic, theoretical, and material-scientific foundations for memory folding, spanning self-organizing cognitive architectures, physical systems capable of encoding historical stimuli, neuro-inspired continual learning, decentralized graph-based memory networks, resource-efficient transformers, hierarchical memory manipulation in LLMs, semantic augmentation in agent systems, hybrid episodic-semantic agents, and reinforcement-learned working memory curation. This article surveys the paradigmatic approaches and theoretical frameworks, tracing the development, mechanisms, and applications of autonomous memory folding.

1. Self-Organizing Memory Architectures

Rooted in the formalism of discrete mathematics and geometric group theory, autonomous memory folding in sensor-based agent architectures (Guralnik et al., 2015) proceeds by transforming raw binary sensory streams into minimal yet semantically rich internal models. The central mechanism involves “snapshot” updates: real-valued edge weights are iteratively refined via local, unsupervised rules encoding statistical co-activation frequencies among sensors. These weights define pairwise implication relations, constructing a weak poc set—a discrete structure encoding subset nestings (sensor $a$ implies sensor $b$ precisely when $a \leq b$).

The pivotal operation is the “coherent projection”, which, for a raw sensory observation $A$, yields the unique minimal, consistent set of features:

$$\operatorname{coh}(A) = \uparrow A \setminus \uparrow A^\ast$$

This folds the high-dimensional sensory input onto a compressed equivalence class, recursively refining distinctions relevant for agent behavior.

The duality between weak poc sets and CAT(0) cubical complexes via Sageev–Roller duality enables transformation of $P_t$ (the weak poc set at time $t$) into a model space $M_t = Cube(P_t)$, with each vertex representing a conflict-free $\ast$‑selection of sensors. Memory folding thereby simultaneously compresses, organizes, and preserves all essential sensory equivalence classes, supporting both semantic abstraction and the operational requirements of planning tasks.

2. Quadratic Complexity and Minimality

The efficiency of autonomous memory folding is reflected in its quadratic resource bounds: space complexity is $O(N^2)$ for $N$ sensors, as every possible pairwise relation requires a counter or weight, and update-execute cycles require $O(N^2)$ time. These bounds hold regardless of sensor diversity or topology, guaranteeing practical scalability as the sensorium expands (Guralnik et al., 2015).

The minimality of the folded internal representation is ensured by the architecture’s selective recording: only witnessed pairwise relationships are encoded, discarding redundant or irrelevant sensory combinations. The cubical complex $M_t$ resulting from weak poc set dualization is thus the smallest possible structure capturing observed equivalence classes, supporting efficient storage and lookup.

3. Topological Fidelity, Learnability, and Precision

Memory folding preserves key topological features of the agent’s environment. While $M_t$ as a complete cubical complex is contractible (as expected from CAT(0) spaces), the sub-complex “witnessed” by the agent’s sensory equivalence classes reflects the true homotopy type of the environment (Guralnik et al., 2015). This ensures that salient navigational properties (such as the presence of holes or passages) survive compression and remain accessible for planning.

Learnability is established via local Hebbian-like update rules, available in empirical or discounted forms, which converge to correct pairwise relations with arbitrary precision as sensory experience accrues. This iterative refinement progressively realizes exact memory folding, resolving all semantic redundancies while preserving predictive distinctions necessary for agent behavior.

4. Physical Systems and Coupled Instabilities

Autonomous memory folding also characterizes certain material systems, notably crumpled sheets subject to mechanical strain (Shohat et al., 2021). These systems encode history via networks of interacting bistable elements (hysterons), whose snap-through instabilities result from local geometric configurations. The global force–displacement response of such a sheet not only retains memory of maximal applied compression but allows the encoding of nested, return point memories—where the system reliably “remembers” and reproduces the precise mechanical configuration at various prior strain maxima.

Theoretical frameworks model these systems as disordered networks of bistable springs with double-well potentials:

$$U_i = \frac{c_i}{4}(\delta r_i)^4 - \frac{a_i}{2}(\delta r_i)^2$$

The collective snapping of hysterons under external strain or cycling yields a physical implementation of autonomous memory folding, with hierarchical, path-dependent configuration spaces analogous to high-dimensional memory graphs.

5. Generative Replay and Continual Learning

Memory folding is a central aspect of lifelong and continual learning. In generative replay architectures (Zhou et al., 2023), artificial neural networks recombine and reorganize previously encoded experiences during offline periods, repairing or “folding” memory traces that have deteriorated from catastrophic forgetting. The integration of generative and classification pathways within a joint VAE framework enables autonomous recovery of latent representations:

$$\mathcal{L}_{total} = \mathcal{L}_r + \mathcal{L}_v + \mathcal{L}_c$$

Offline self-training on replayed samples results in hidden representations that realign with the state immediately following initial acquisition, as measured by metrics such as centered kernel alignment (CKA). Quantitative results indicate substantial improvements in task accuracy and recall, often exceeding 20% gains in continual learning benchmarks, particularly in domain- and class-incremental settings.

6. Distributed and Decentralized Graph-Based Memory

In decentralized architectures inspired by the biological engram theory (Wei et al., 2023), memory folding emerges from parallel, in-node distributed algorithms operating on active-directed graphs. Each node—representing a neuron—propagates and records activation traces based solely on local context, resulting in connected subgraphs (engrams) encoding memory. Sparse connectivity yields high capacity, as memory storage is a permutation of weakly connected components ($\text{WCCs}$), allowing networks with $500$ nodes to sustain thousands of samples with high resilience against node or edge faults. This distributed memory folding provides critical robustness and concurrency, emulating features of biological neural systems.

7. Folding Attention and Resource-Efficient Representations

Memory folding in transformer architectures is realized via folding attention mechanisms (Li et al., 2023), optimizing for on-device inference under tight memory and power constraints. Here, token embeddings of dimension $D$ are folded into $N$ sub-tokens, processed via reduced-size linear projections and reassembled via unfolding operators. This reduces model size and consumption by factors of $1/N$ (computation) and $1/N^2$ (parameter count), achieving a 24% reduction in memory and 23% in power, with negligible performance impact, as shown in speech recognition benchmarks. This architectural folding enables the deployment of transformer models in edge and mobile environments where traditional memory management methodologies are impractical.

8. Hierarchical Embedding Augmentation and Structural Manipulation

LLMs increasingly leverage hierarchical embedding augmentation and dynamic memory reallocation (Yotheringhay et al., 23 Jan 2025). Token representations become weighted sums over multiple semantic layers:

$e_t = \sum_{l=1}^L \alpha_{t,l} \cdot v_{t,l}$

with attention weights $\alpha_{t,l}$ computed from layer-wise similarity scores. Dynamic reallocation via hierarchical clustering prioritizes critical features and suppresses superfluous tokens, reducing processing overhead by up to 45% for long input sequences. These organizational principles facilitate robust task generalization, adaptivity, and interpretability, especially in multi-domain and interactive contexts.

9. Semantic Augmentation, Episodic–Semantic Hybrids, and RL-Based Folding

In agentic systems incorporating structured semantic augmentation (Salama et al., 27 Mar 2025), autonomous memory folding involves extraction and annotative prioritization of key attribute–value pairs from historic interactions. Embedding-based retrieval (using systems such as FAISS), combined with contextual prioritization algorithms, significantly improves persuasiveness, recall, and context alignment. Hybrid memory architectures for low-code agents (Xu, 27 Sep 2025) combine episodic and semantic stores, using proactive “Intelligent Decay” mechanisms grounded in recency, semantic relevance, and user utility:

$$S(M_i) = \alpha \cdot R_i + \beta \cdot E_i + \gamma \cdot U_i$$

This structure ensures capacity management and contextual consistency for agents operating over hundreds of turns, surpassing sliding-window and basic retrieval-augmented generation approaches.

Memory-as-action formulations (Zhang et al., 14 Oct 2025) recast context curation as an RL-optimized intrinsic capability. Agents actively edit working memory through retention, compression, and deletion actions, with learning driven by task reward signals and resource penalties, yielding robust, adaptive, end-to-end context management via Dynamic Context Policy Optimization. This algorithm segments trajectories at memory action points, stabilizing gradient updates in the presence of non-monotonic context histories.

10. Applications and Implications

Autonomous memory folding finds applications in adaptive robotics, continual-learning systems, material-based memory devices, neuromorphic and graph-inspired hardware, long-duration agentic systems, resource-constrained transformer deployment, knowledge management, recommendation, multi-hop question answering, and real-time decision support. Robustness, scalability, and the ability to reorganize context or memory without external input or supervision are critical in dynamic, unpredictable, and resource-bounded environments.

These approaches collectively establish autonomous memory folding as a foundational capability for the next generation of adaptive intelligent systems, encompassing theoretical, algorithmic, and empirical advances in the efficient, self-organizing management of experience and knowledge.